Liquid-junction potential, calculation

The liquid junction potential calculated with this equation should not be used for very accurate applications. The conditions assumed in its derivation are never all fulfilled in practice. The main assumption, that the participating ions migrate exclusively according to the concentration gradients so that pure diffusion results, is seldom valid. This is true especially for the common reference electrode constructions in which convection of the electrolyte arises (this is desired for other reasons). In addition, in order to calculate the individual ion activities one needs the individual activity coefficients, and these are not accessible through experimental measurements (as shown in the Appendix). In practice, the analytical applications ofEMF measure-... 

Electrochemical methods covered in this chapter include poten-tiometry, coulometry, and voltammetry. Potentiometric methods are based on the measurement of an electrochemical cell s potential when only a negligible current is allowed to flow, fn principle the Nernst equation can be used to calculate the concentration of species in the electrochemical cell by measuring its potential and solving the Nernst equation the presence of liquid junction potentials, however, necessitates the use of an external standardization or the use of standard additions. 

An electrode potential varies with the concentration of the ions in the solution. Hence two electrodes of the same metal, but immersed in solutions containing different concentrations of its ions, may form a cell. Such a cell is termed a concentration cell. The e.m.f. of the cell will be the algebraic difference of the two potentials, if a salt bridge be inserted to eliminate the liquid-liquid junction potential. It may be calculated as follows. At 25 °C ... 

Difference with respect to value calculated from accepted standard potential and activity coefficient is attributed to liquid junction potential. 

Here, x is the coordinate normal to the diaphragm, so that d — q—p. The liquid junction potential A0L is the diffusion potential difference between solutions 2 and 1. The liquid junction potential can be calculated for more complex systems than that leading to Eq. (2.5.31) by several methods. A general calculation of the integral in Eq. (2.5.30) is not possible and thus assumptions must be made for the dependence of the ion concentration on x in the liquid junction. The approximate calculation of L. J. Henderson is... 

So far, a cell containing a single electrolyte solution has been considered (a galvanic cell without transport). When the two electrodes of the cell are immersed into different electrolyte solutions in the same solvent, separated by a liquid junction (see Section 2.5.3), this system is termed a galvanic cell with transport. The relationship for the EMF of this type of a cell is based on a balance of the Galvani potential differences. This approach yields a result similar to that obtained in the calculation of the EMF of a cell without transport, plus the liquid junction potential value A0L. Thus Eq. (3.1.66) assumes the form... 

To leam about how a liquid junction potential, j, arises, and appreciate how it can lead to significant errors in a calculation which uses potentio-metric data. 

So by poor experimental design, we have allowed a liquid junction potential to form in our cell. While we have the same emf as in the first cell, in fact the activity of copper ion in this new cell is only 9.5% of the activity calculated for the case where no liquid junction potential was induced. 

An electrode potential Eaq+.aq is measured as 0.670 V. In fact, this value is too high because the value of Eaq+.aq also incorporates a liquid junction potential of 22 mV. Calculate two values of a(Ag ), first by assuming that Eaq+.aq is accurate, and secondly by taking account of E. What is the error in a(Ag ) caused by the liquid junction potential Take E + = 0.799 V at 298 K. 

When considering potentiometric errors, it is necessary to appreciate how a liquid junction potential, Ej, arises, and appreciate how such potentials can lead to significant errors in a calculation. In addition, we saw how the IR drop can affect a potentiometric measurement (and described how to overcome this). Finally, we discussed the ways that potentiometric measurements are prone to errors caused by both current passage through the cell, and by the nature of the mathematical functions with which the Nemst equation is formulated. 

The experimental apparatus consists essentially of a narrow vertical glass tube down the inner surface of which one liquid is made to flow, the other liquid emerges from a fine glass tip in the form of a narrow jet down the axis of the tube. The two solutions are connected with calomel electrodes employing potassium chloride or nitrate as junction liquids. The E.M.F. of the cell is measured by means of a sensitive quadrant electrometer. The greatest source of error in the method is the elimination of or the calculation of the exact values of the liquid-liquid junction potentials in the system. For electrolytes which are not very capillary active, the possible error may amount to as much as fifty per cent, of the observed E.M.F. 

Hence, pH is not identical with — log H+ since the calculation of ycr is somewhat arbitrary. Furthermore, an unknown difference in liquid junction potentials may become important especially if solutions X and S differ in ionic strength and composition. Using a medium of constant ionic strength, however, it is possible to determine the hydrogen ion concentration, [H+], using a glass or hydrogen electrode. Biedermann and Sillen (8) extensively studied the cell ... 

For a uni-univalent electrolyte, the multiplier term in (6.24) cancels out and the liquid junction potential can be calculated from the equivalent ionic conductivities Xi of the two solutions, from the Sargent equation. 

Correct measured values for liquid junction potentials using the Henderson formalism and calculate ion activities according to the Debye-Huckel approximation. 

Therefore the fraction of the total cell potential due to the junction potential cannot be unambiguously assigned. However, it is possible to estimate junction potentials indirectly or to make calculations based on assumptions about the geometry and distribution of ions in the region of the junction. For a junction between two dilute solutions of the same univalent electrolyte (concentrations C] and C2), the liquid-junction potential is described by... 

Cells with Liquid Junctions and Elimination of Junction Potentials. When electrochemical cells are employed to obtain thermodynamic data, high accuracy ( 0.05 mV) requires the use of cells that are free from liquid junction (in the sense that the construction of the cell does not involve bringing into contact two or more distinctly different electrolyte solutions). Otherwise, the previously discussed uncertainties in the calculation of liquid-junction potentials will limit the accuracy of the data. 

Table 2.1 lists half-reactions for electrodes of the second type and their potential for unit activities. These electrodes have, in the majority of cases, their own electrolyte associated with them. So, to calculate the potential of a cell in relation to the standard hydrogen electrode it is necessary to take the liquid junction potential between the two electrolytes into account (Section 2.10). 

The liquid junction potential sr is in this case calculated according to the formula... 

For the purpose of exact calculation of the liquid junction potential according to the last mentioned equation the activity coefficient of the hydrogen or chloride ions would have to be known. As their value is unknown it is assumed that their ratio is equal to the ratio of the mean activity coefficients of hydrochloric acid, or in other words ( +)2/( +)i — (a+)2l(a )v Then the equation (VI-28) will be written in this form ... 

Interface between two liquid solvents — Two liquid solvents can be miscible (e.g., water and ethanol) partially miscible (e.g., water and propylene carbonate), or immiscible (e.g., water and nitrobenzene). Mutual miscibility of the two solvents is connected with the energy of interaction between the solvent molecules, which also determines the width of the phase boundary where the composition varies (Figure) [i]. Molecular dynamic simulation [ii], neutron reflection [iii], vibrational sum frequency spectroscopy [iv], and synchrotron X-ray reflectivity [v] studies have demonstrated that the width of the boundary between two immiscible solvents comprises a contribution from thermally excited capillary waves and intrinsic interfacial structure. Computer calculations and experimental data support the view that the interface between two solvents of very low miscibility is molecularly sharp but with rough protrusions of one solvent into the other (capillary waves), while increasing solvent miscibility leads to the formation of a mixed solvent layer (Figure). In the presence of an electrolyte in both solvent phases, an electrical potential difference can be established at the interface. In the case of two electrolytes with different but constant composition and dissolved in the same solvent, a liquid junction potential is temporarily formed. Equilibrium partition of ions at the - interface between two immiscible electrolyte solutions gives rise to the ion transfer potential, or to the distribution potential, which can be described by the equivalent two-phase Nernst relationship. See also - ion transfer at liquid-liquid interfaces. 

Due to the different mobilities, concentration gradients and thus potential gradients will be established. In actual measurements these potentials will be added to the electrode potentials. A calculation of liquid junction potential is possible with the -> Henderson equation. As liquid junction potential is an undesired addition in most cases, methods to suppress liquid junction potential like -> salt bridge are employed. (See also -> diffusion potentials, -> electrolyte junction, -> flowing junctions, and -> Maclnnes.)... 

Morse (21) recently reported near-equilibrium pH-stat rates in sea water at 25°C and 10 atm CO2. His rates are all less than 8 mg cm yt . Table III compares our calculations (using equation 15 and assuming surface PCO2 is equal to the bulk fluid value) of a set of Morse s rates near equilibrium, and shows generally poor agreement. In calculation of Q and aH (s), no correction for liquid junction potential error in measured pH was necessary, as in our earlier calculations for pseudo-sea water. 

In many instances, however, it has not yet been found possible to avoid a junction involving different electrolytes. If it is required to know the e.m.f. of the cell exclusive of the liquid junction potential, two alternatives are available either the junction may be set up in a reproducible manner and its potential calculated, approximately, by one of the methods already described, or an attempt may be made to eliminate entirely, or at least to minimize, the liquid junction potential. In order to achieve the latter objective, it is the general practice to place a salt bridge, consisting usually of a saturated solution of potassium chloride, between the two solutions that w ould normally constitute the junction (Fig. 70). An indication of the efficacy of potassium chloride in reducing the magnitude of the liquid junction potential is provided by thf. data in Table XLVII 3 the values iucorded are the e.m.f.of the cell, with free diffusion junctions,... 

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